Riabov G. Finite absolute continuity of measures on infinite dimensional spaces

The thesis is devoted to the investigation of finite absolute continuity of measures on infinite dimensional spaces. Criterions of finite absolute continuity for product-measures on the space of sequences are proved. The sufficient condition of finite absolute continuity of measures defined as mixtures of regular families of conditional measures on the product of Banach spaces is obtained. The necessary and sufficient condition of finite absolute continuity of Gaussian measures on separable Frechet space is proved. Shifts along the basis of the measure on infinite dimensional abstract Wiener space with p-summable imbedding operator which is finitely absolutely continuous with respect to initial Gaussian measure are defined and their weak convergence is proved.